Question

A solid sphere of mass M and radius R has a spherical cavity of radius $\frac{R}{2}$such that the centre of cavity is at a distance $\frac{R}{2}$from the centre of the sphere. A point mass m is placed inside the cavity at a distance $\frac{R}{4}$from the centre of sphere.
The gravitational force on mass m is

(a) $\frac{11GMm}{R^2}$ (b) $\frac{14GMm}{R^2}$ (c) $\frac{GMm}{2R^2}$ (d) $\frac{GMm}{R^2}$

Answer 1

Dear student
$$\begin{gathered} gravitationalfieldinthecavityis \\ E=\frac{4\pi G\rho }{3}(\left|{\overrightarrow{C_{1}C}}_2\right|)(C_{1}and{C}_{2}arethecentresofthesphereandthecavity) \\ \rho =\frac{M}{{\displaystyle \frac{4}{3}}\pi R^3}and{C}_1{C}_2=dis\tan cebetweenthecentres=\frac{R}{2} \\ E=\frac{4\pi G\times M}{3\times {\displaystyle \frac{4}{3}}\pi R^3}\left(\frac{R}{2}\right) \\ E=\frac{G\times M}{R^2}\left(\frac{1}{2}\right) \\ soforceactingonthechargeis \\ F=mE \\ F=\frac{G\times m\times M}{2R^2} \\ Regards \end{gathered}$$